If the Corp plays Anonymous Tip, do they draw all the cards at once and then decide which ice to install with Jinja City Grid, or do they draw the cards one at a time and decide as ice is drawn whether or not to install any of those ice?

Drawing multiple cards at once is a batch effect. The Corp draws all three cards, then Jinja City Grid meets its trigger condition simultaneously for each drawn piece of ice. The Corp decides the order in which to trigger the instances of Jinja City Grid's ability, and thus the order in which to install the drawn ice.

If the Runner initiates a run on a server with Jinja City Grid and the Corp has a scored Advanced Concept Hopper, will the Runner approach an ice drawn with Advanced Concept Hopper and installed with Jinja City Grid?

Yes. Advanced Concept Hopper meets its trigger condition at step 1 of the run, so by the time the Runner begins approaching ice in step 2, the newly installed piece of ice will be the outermost piece.

If the Corp has both Jinja City Grid and Daily Business Show rezzed, and they draw two pieces of ice, can they install both pieces of ice and avoid putting one on the bottom of R&D?

No. The game still knows that those were the two cards drawn with Daily Business Show, so the Corp must put one of the installed pieces of ice on the bottom of R&D.

The powerlevel of this card may just be a little over the top, but maybe thats exactly what Glacier needs.

1 rez, 5 trash is comparable to e.g. Jeeves Model Bioroids, which as well can (combined with other cards and actions) result in some serious tempo gain and thus often is a must trash. It's an asset though.

Long story short, in combination with massive card draw effects Jinja City Grid is a huuge boost to Glacier style decks. These decks excel in taxing runners out. Add in a little Bryan Stinson, who really pushes those clearances over the top and you got yourself a tier 1 Glacier deck.

Runners beware you will have to deal with not only horizontal but also vertical spam in the near future (looking at you Anarch).

This will create some out of control servers. 5 ICE deep servers for free. A savings of 9 credits after factoring Jinja's rez cost. And since the credits aren't recurring credits, you can do this very fast. The price of course is giving the runner full knowledge of the ICE installed.
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quailman21017 Feb 2018

Full knowledge means nothing when the tax is real. This out of ASA (with tons of upgrades as I've been playing it) will be tough to deal with.
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LynxMegaCorp7 Feb 2018